New clean-energy technologies reducing greenhouse effect may be based on controlled burning of lean gas mixtures in the “excess enthalpy” combustors. In particular, the lack of knowledge on combustion mechanisms and flame stabilization in the systems with heat and mass recirculation hampers the progress in further developments of “mild” or HiCOT, high temperature oxygen combustion technologies that allow reduction CO2 emission and increasing efficiency of industrial power plants. This leads to the further requirements of fundamental studies on the combustion with a large amount of CO2 and the absence of nitrogen at elevated temperature and pressure. Theoretical and experimental study (including experiments in microgravity conditions) of these processes will fill a gap in our knowledge about reduced chemical reactions kinetic mechanism, transport processes, radiative heat losses and dynamics of the self-fragmented (or sporadic) combustion waves. The actual problems of combustion theory related with modeling of flame dynamics near flammability limits, developments of micro combustion technologies and gas combustion in porous media are discussed.